How to Debate Beauty

How to debate Beauty

[cosmic variance. Gina Says: May 10th, 2007 at 6:18 am ] The issue of beauty and physics is quite prominent in this discussion. Lee Smolin warns against adopting a physics theory based on aesthetic consideration and brings Kepler’s theory relating the five planets and five platonic solids (regular polytopes) as an example. Peter Woit makes (repeatedly, again and again and again) the claim that string theory is simply ugly, very ugly.

Well, beauty is a subjective matter. I remember my dear grand uncle Lena telling me:” Gina, aren’t we very lucky that people see things in a subjective way? If men were objective they would have all fallen in love with my own beloved wife (her name was incidentally also Gina,) who is clearly the most beautiful woman. This could have caused all sorts of complications.”

I, for example, regard string theory as very beautiful. Supersymmetry which grew up along string theory is an extremely beautiful notion. (In my view, supersymmetry has a natural form of beauty while string theory has an exotic and peculiar beauty.)

But the really interesting question in my mind is how to debate beauty. Can beauty be argued and debated at all?

Here is a story about arguing beauty in court, which may be of use. It was a case where the defendant was accused of a terrible crime.

The attorney for the defendant said in his opening speech: “Look at the defendant. Look how beautiful he is and look at his blue eyes, eyes of an angel. Do you really think he is capable of committing this ugly crime?”

At first, the prosecutor thought of ignoring this remark altogether, but then the remark was repeated and similar sentiments were expressed by some witnesses. The prosecutor watched how this non-issue was becoming an issue, and was worried that the beauty claims might convince some jury member.

The dilemma was not a simple one. Trying to argue that the defendant was not beautiful might convince a few jurors but would strengthen the belief of others that having beautiful eyes is indeed an impediment to being a criminal. Trying to argue that there is no connection between the innocent angel look and the crime may give this whole beauty business some credibility, and may cause those jurors who believe in this connection to take for granted that the defendant is indeed beautiful.

This is what the prosecutor said in his closing argument:

“Ladies and gentlemen of the jury,” said the prosecutor, “there are two types of beauty. There is beauty that reveals a beautiful soul and there is beauty that covers up a corrupted and distorted personality. It is very difficult to distinguish between these two types of beauty, and often our initial hunches and intuitions turn out to be wrong.

We have carefully proved during this trial that the defendant committed the crime he is accused of, and therefore you must conclude that to the extent you find him beautiful, this is beauty of the bad kind, beauty which covers a corrupt personality capable of committing terrible crimes.”

Can I answer a question with as question? Do you remember ever changing your mind about whether something was beautiful? What made you do so? (In my case, I think that, with maybe one or two trivial exceptions, were I hadn’t really looked carefully first, all of my experiences were of deciding that things were more beautiful than I had a realized.)

I am afraid I heavily disagree with you. In order to understand the concept of beauty in physics, you have to be a theoretical physicist. This is necessary but not sufficient. You must be able to ponder into the depth of *first-principles* in special relativity electromagnetism, gravity and Yang-Mills (to say the least), and I think that very few of my fellow theoreticians do that these days. We are living in an era of technical capabilities, and people tend to loose their way in grammar and syntax. As you wrote in your excellent expository “Gina says”, abstract mathematics is a machine language, but in physics you need a much more sophisticated language (say MATEMATICA compared to machine language).

Being an ex-theoretical physicists, I myself find ST conceptually and philosophically ugly. The underlying mathematics may be nice and rich but it is based on machine language and therefore, as its stands, it cannot produce the beauty of the first principles, and their interrelations. ST pretends to be a TOE but it haven’t supply us with a single new first principle we didn’t know before. At present, nobody knows what is means non-perturbatively, it is partially inconsistent with the objective beauty of theories we are already very much familiar with (objective indeed!), and of course, it has nothing to do with nature (being a theory in 9+1 (or 10+1 in M-theoey) spacetime dimensions, probably a consistent theory). Supersymmetry is indeed a beautiful concept and mathematical structure, but, in my humble opinion (and some others as well), the way it is embedded into current physical theories is ugly indeed.

I think your grand uncle Lena was wrong (but I’m sure he was very clever…). If his wife was very beautiful to his eyes, she was probably also very beautiful in the objective sense. It is possible that she was not that beautiful, but he simply loved her and therefore saw her beauty *in spirit*. It is not that all men agree on a women’s beauty. But when a really beautiful woman shows-up *everybody* holds its breath.

Dear Shmuel,
Hmm, I think I have a similar experience regarding beauty and hardly ever (or never) changing my mind at least from the direction beautiful –> ugly.

Dear Nivra,
I checked the records regarding Gina’s great uncle Lena and it turned out that “objective” is the wrong word and indeed the wrong concept. What Lena said was “Thank God that people have different *TASTES*, otherwise they would all love Gina. “(Gina was also his wife’s name). Regarding string theory I think people have different tastes as well. I do not have any first-hand opinion, but i did listento people who described the theory and I could sense and identify with their feeling of beauty and coherence.

Beauty is more fundamental than taste. Some people like quantum mechanics in the Schrodinger picture, others in the Heisenberg picture. This is taste. The beauty of the theory, however, (as a physical theory explaining, for example, the emission spectrum of the Hydrogen atom) is deeper than any specific representation of it.

When a string theorist says that he finds ST coherent and beautiful, I know there is something there that cannot be shared by the layman. When a mathematician tells me that Category theory is a beautiful setup, I am sure he knows what he is talking about. In order to be able to see the real beauty of a theory, you need to be an expert in the field. Otherwise, your view is a layman’s view, shallow and partial.

And this is the point I am trying to make: non-physicists are not in a position to select a physical theory according to their taste. The same applies to non-mathematicians in mathematics. This privilege is saved for those who can see things at all levels: the experts in their field.

I’ve certainly changed my mind in the direction beautiful->ugly. Sometimes, I listen to a song which sounds amazing in a language I don’t understand. A few years later, maybe I speak more of the language, and the song sounds awful. I suppose it’s because, when I think something is beautiful, I want to learn more about it, and once I do, it may turn out never to have been beautiful in the first place after all. There is mystique in what is unknown- when it is known, it may turn out to be ugly, or bland. Think of beautiful mountains shrouded in mist… but when the mist rises, the mountains may look ugly.

Another example is thinking something is beautiful because somebody else suggests that this is so. Then, when one looks at it again, it may look ugly.

I don’t know if I’ve changed my mind in the direction beautiful->ugly as often as in the direction beautiful->bland. Sometimes, when you don’t know something very well, it looks really beautiful, but once you begin to understand it it seems bland. An example is Euler’s identity, which I once thought was beautiful (because everyone else said so), and which I now think is completely dull. Or multiplication of fractions.

I think ST is, at the very least, not ugly- it has after all given rise to beautiful mathematical ideas.

I don’t think I understand nivra’s categorical claims (maybe I am caricaturing them?) that to find a physical theory beautiful (in a “deep” sense, whatever that is) one must be a physicist. I find Yang-Mills theory, and especially the way it emerges from a few basic physical principles (e.g. gauge invariance + the Lagrangian formalism), very beautiful, but I am not remotely a physicist. I would even distinguish the beauty I see in this physical theory from the way in which I find Chern-Weil theory beautiful (even though the theories overlap in many ways). For that matter, I find many mathematical theories beautiful in areas in which I am not an expert – probability, combinatorics, number theory, etc. I think that many geometers (for example) think very deeply and profoundly about space(s), sometimes in ways that have a lot in common with what is sometimes called “physical intuition”, and that they have the capacity to respond to some of what is called beautiful in string theory in terms which are not completely dissimilar to the way that some physicists see it. Well, in the end I am not a physicist, so perhaps I am missing the basic point here (maybe this is a bit like appreciating art or literature that arises in a culture outside one’s ken . . .)

I find the analogy that mathematics is machine language whereas physics is Mathematica quite opaque; perhaps you could elaborate? (incidentally, Mathematica is one of the few things listed above that I really do find ugly . . .)

By the way, this touches on an interesting question, namely: who is an expert, and is it even desirable to be an expert? I remember Dick Gross telling me a story about attending a lecture that Serre gave, in which someone asked a question, and Serre answered, but with a “disclaimer” that he “was not an expert”. Now, this was a question in a field that Serre had more-or-less invented – what did he mean by saying he was not an expert? Apparently (according to Gross), Serre used the term “expert” quite disparagingly, to refer to people whose focus was so narrow that they only knew (or cared) about one thing.

Consider the physical principle: “all inertial observers are physically equivalent”. In down-to-earth words, this means that nature does not distinguish the state “being at rest” from the state “moving in speed 299,000 kilometer per seconds” (with respect to “being at rest”). This is a very deep principle and more or less the whole theory of special relativity emerges from it. Then comes the mathematical beauty: formulate physical theories in a frame-independent manner (because it is frame-independent).

Now, the first pair of Maxwell equations follows exclusively from three properties: a) there is a substance called electric charge, b) electric charge radiates its influence through space, and c) electric charge is conserved. If you impose the constraint on the lack of magnetic charge you get the 2-nd pair (I shall skip the details). Then, if it is combined with the principle that all inertial observers are physically equivalent, you get a relativistic theory which appears to be local gauge symmetry for wave functions. In such a theory (in general) force is associated with the curvature of the some symmetry space…

The EM theory, in its most elegant and aesthetic structure, starts from scratch and evolves into a mature and comprehensive paradigm by applying appropriate mathematical gadgets.

Of course, there are many mathematicians with very good sensation for good physics. I am sure that as a geometer you may easily appreciate the beauty of YM, but where will you take it from here? Can you find the underlying physical principle that sews GR with QFT to get QG? Or perhaps find a structure that replaces GR+QFT by QG? Can you find the principle that brings us closer to GUT? How will you extract new first-principle from experiments and observations? And how will you be able to pick-up the right idea from a bath filled with countless ideas and a lot of good will?

If you will try to do that, you might come-up with something as sophisticated as ST. You may then highly appreciate the mathematical beauty of your newborn but, alas, it will probably have nothing do with the ‘real’ word. And you might even not notice that it is incompatible with first principles that you have already learnt to appreciate.

Finally, regarding the last paragraph of your comment, an expert in a field is the one who knows many of its aspects, and from various perspectives. I think this is a sensible definition. Sometimes this gives him the tools to understand things that go beyond his field of expertise, but probably only from a limited angle.

Right! it is indeed correct that Plato would view the ideal of beauty to be more fundamental then tastes regarding beauty…

The story in this post as, to a large extent, of my book itself was meant to take some interesting issues from the specific context of the heated blog debate away from string theory and even away from physics. And indeed the issue of debating beauty is quite wider.

(Therefore, I could not understand what the statement “I am afraid I heavily disagree with you” refer to.)